For the most part leaving apps in the recently used list of the multitasking bar will not increase battery consumption. Some apps will run background tasks which can increase battery use although Apple does limit background use. With that said some apps such as Waze GPS app can run in the background keeping the GPS running which will drain a battery fast. But if properly turned off it too can stay in the recently used apps without consuming battery.

One issue though is occasionally an app may not properly go to sleep and may continue to run processes in the background causing excessive battery drain and/or poor performance. If you do see a drastic increase in battery consumption you can usually fix it by closing all the apps in the multitasking bar then resetting the iPhone by powering it off then restarting it. This can happen on all iOS devices.

I can tell you that I have yet to fully "close" a single app on my iPhone 5 since owning it for over a month now. I have over 50 apps in the multitasking bar yet my battery life is not affected. As previously stated, some apps may go "rogue" and cause issues such as extreme data usage and battery draining. Facebook has been know to cause problems on iOS (iPhone, iPad, and iPod touch) and even Android. There used to be a bug in the Mail app back around iOS 4 that would drain devices if they were connected to a network and left the app running. Apple has since fixed that issue but Facebook is still a culprit from time to time.

All-in-all, it is not necessary to fully close apps. They are put in a suspended state after you are done with them and don't consume excess computing cycles. Some apps do update in the background (Mail is an example) but many of these apps don't need to be open to actually update. Facebook, Mail, etc. can all be fully closed yet still receive updated content as part of built-in iOS functionality.

The only app I've had a problem with is Facebook - sometimes when it's on the task bar, it drains the battery faster. I've tested this with Facebook being the only app on the task bar. This is on the iPhone 5, which I have found to have about the same or maybe even slightly better battery life than the 4S.

- Whether or not an app is in the task bar or not has virtually no bearing on whether or not it's still "on" as iOS kills background apps the instant it needs more RAM for an active process, so you "killing" those apps past the first 3 or 4 on the task bar cannot possibly be doing anything as they're already as closed as they're going to get.

- Whether or not an app is in the task bar, or has even been launched since your last reboot, has no bearing on most of its background tasks. These run automatically based upon your notification settings, so if an app is allowed to send you push notifications, or to use location aware services, it is running the necessary background routines and powering on and off the bluetooth or wifi antennae as necessary to accomplish this regardless of its "on" status.

- Because even the best of the iOS devices has relatively little RAM, it's pretty much a given that ~100% of RAM is occupied any and all times the device is not in powered down mode and drawing whatever power is associated with maintaining that amount of information in RAM unless you are religiously always killing 100% of all apps after you're done, and even then, I'd point out that plugging your device in more often is going to take a lot less time and effort than constantly killing apps.

- In a related vein, since current iOS devices are packing some fairly competent processors, outside of complex and/or graphically intensive active apps, the processor and GPU units aren't taxed much at all even for active apps. So, battery drain is minimal from the actual running of most active apps and, relatively speaking, nothing at all from the sort of stuff that goes on in background tasks.

- Speaking of background tasks, regardless of your intentional app usage, iOS itself is doing tons of things in the background that you have no control over short of turning your wirelessly connected smart device into the equivalent of a fancy looking iPod classic.

- Most importantly, the number one thing draining your battery is the screen. If your screen is on, even to just look at the springboard, it's draining more juice than every background wifi, bluetooth, mail check, message check, photostream upload, holding status in RAM, your crops are ready push notification combined.

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tl;dr: In other words, religiously killing background apps can hypothetically save a teeny tiny insignificant amount of battery related to holding the process in a suspended state in RAM. However, even assuming you're doing this 100% of the time, it is nothing compared to what your screen is using. Turning down the brightness a little bit or checking your device a little less often is going to go a lot further for saving battery life than any killing of tasks ever could.